Chris Anderson Pat Kirell

Transcription

1 You want me to Excuse your Dear Aunt Who for What?! Activities to Enhance the Order of Operations Grade Level: 7 10, with some modifications for primary students. Introduction: This packet/lesson has been created to help teachers teach the order of operations. In this packet, you will find the guided notes and practice for students as well as four activities to enhance their understanding as well as get away from the traditional teaching style. Please feel free to change the material to suit the grade level that is being served. Standards: New York State MST Standard #3 -Operations: 3. Students use mathematical operations and relationships among them to understand mathematics. Students: add, subtract, multiply, and divide whole numbers. develop strategies for selecting the appropriate computational and operational method in problem solving situations. know single digit addition, subtraction, multiplication, and division facts. Objectives: After this lesson, students should be able to perform the order of operations on given sets of numbers and in given mathematical statements and equations Instructional Protocol: The guided notes are basically there to show students how problems are to be done and give teachers handouts to use when teaching PEMDAS. Do not plan on doing all of these activities in a single block class. This packet is meant for you to choose an activity to do on a certain day. None of the following activities will take a full class period to complete. Use the Internet links to find websites that I find helpful to my students. This is not the end all lesson for the order of operations. Please modify it and use it when and if you need it. Chris Anderson Pat Kirell

2 Lesson: Order of Operations Guided Notes Order of Please Excuse My Dear Aunt Sally Always go from Left to Right Examples: Simplify: 80 4(7-5) Simplify: 6(4 + 1) 2 + (8 5) 3 Simplify: (8 7) x 3 Simplify:

3 Guided Practice: Work on the following problems in groups of 2 or 3. Ask questions when you have something that is confusing to you (2 + 5) 50(6) (5 + 4) (18-9) (6-1) 3 20 (25 5) [7 (2 + 3)] (7 5) (4 + 10) 2

4 Activities Bowl A Fact Need: 4 dice Set of plastic bowling pins Rules: Students are given 3 dice. Plastic bowling pins will be set up labeled One student rolls all three dice and uses those three numbers* using any operations to reach one of the pin numbers. If a number is reached, the pin is knocked down. Students knock down as many pins as possible with the first three numbers and are allowed a 2 nd roll if all the pins are not knocked down. Object: Knock as many pins down as possible. Ex. Dice are rolled and 3, 1, 6, and 4 come up Need to obtain all number from 1 to * = 7 3 * = 5 3/1 * 4 6 = /1 6 = = 2 and so on until all 10 numbers have been taken away. If all ten cannot be taken away, then the student rolls a second time to try and pick up the spare. Scoring ( Here are three examples of scoring for bowling EXAMPLE 1 Frame John Score In Example 1 we omitted strikes and spares for simplicity. Each frame is totaled and added to the cumulative score. EXAMPLE 2 Frame Mary 9-0 3/ 6-1 3/ 8-1 5/ 0/ 8-0 7/ 8/8 Score In Example 2 we learn how to score spares and open frames together. A spare is scored as 10, plus the pinfall of the next ball rolled. This total is added to the cumulative score. Frame 1) Count 9 pins Frame 2) Spare (10), plus next ball (6) added to score = 25 Frame 3) Count 7 pins and add to score = 32 Frame 4) Spare (10), plus next ball (8) added to score = 50 Frame 5) Count 9 pins and add to score = 59 Frame 6) Spare (10), plus next ball (0) added to score = 69 Frame 7) Spare (10), plus next ball (8) added to score = 87

5 Frame 8) Count 8 pins and add to score = 95 Frame 9) Spare (10), plus next ball (8) added to score = 113 Frame 10) Add (10), plus 8 to score = 131 Example 3 Frame Kim X 3/ 6-1 X X X 2/ 9-0 7/ XXX Score In Example 2 we learn how to score strikes, spares and open frames together. As previously demonstrated, a spare is scored as 10, plus the pinfall of the next ball rolled. A strike is scored as 10, plus the pinfall of the next 2 balls rolled. This total is added to the cumulative score. Frame 1) Strike (10), plus next 2 balls (3)(7) = 20 Frame 2) Spare (10), plus next ball (6) added to score = 36 Frame 3) Count 7 pins and add to score = 43 Frame 4) Strike (10), plus next 2 balls (10)(10) add to score = 73 Frame 5) Strike (10), plus next 2 balls (10)(2) add to score = 95 Frame 6) Strike (10), plus next 2 balls (2)(8) add to score = 115 Frame 7) Spare (10), plus next ball (9) added to score = 134 Frame 8) Count 9 pins and add to score = 143 Frame 9) Spare (10), plus next ball (10) added to score = 163 Frame 10) Strike (10), Strike (10), Strike (10) = 193 This game can be played over a ten day period (1 frame per day) or can be used as a math warm-up or filler activity. *primary students get to pick 2 numbers instead of 3 Target Number and Number Squeeze(everyday math game) Target Number $$All numbers cannot be solved for exactly$$ Need: 5 dice Level: Any level after talking about order of operations Object: To make a number as close to a given number as possible Procedure: 1. You need 5 dice 2. Roll two of the dice and choose the number you want(ex. If a 3 and 5 come up you can use 35 or 53(target number)). 3. Roll all 5 dice 4. The students have to use the 4 numbers that come up and perform math operations to try to get as close as they can to the target number. They are only allowed to use each number once. They are to use any operation including squares and square roots. 5. Give the kids one minute to work. When time is up, whoever is closest gets a point. If more than two kids are the closest, then both get a point but the students must have the

6 work written down to get credit. If a student should get the target number while working, he must yell out TARGET indicating that he/she got it. If they did the work correctly, then they get 2 points and you start all over. An example Target number: 45 Numbers Rolled: 1, 3, 5, 6 (6+3) * 5/1 = 45 If a student uses an exponent, it must be one of the numbers, which would make two numbers gone. Another way to play this game is to use playing cards instead of dice. In Primary instead of dice, to select target number teacher will have pre-made target numbers to control level of difficulty (goal will be closest to number). Number Squeeze Need: 2 yardsticks or tongue depressors per pair of students 2 large graphics of your choice (hands) per pair of students number line (large for a group, small for individual) Make two hands (or graphics of your choice). Attach them to the end of yardstick or tongue depressors. Pick a secret number on the number line. One student covers up a number that comes before your number and another student covers a number that comes after your number. Ex. Magic #9 Student #1: Is you number bigger than 6? - Yes, they put their left hand (BOLT) on the Student #2: Is your number bigger than 11? - No, they put their right hand (BOLT) on Continue this process until the only number left is 9.

7 Smadness** Need: 4 dice Object: Create the numbers 1 10 using four numbers rolled Procedure: 1. Students are separated into 2 or more teams and a team leader is selected. 2. All 4 dice are rolled simultaneously, giving us 4 distinct numbers 3. Teams use the four numbers rolled and the order of operations to create the numbers from When a team has found all of the digits, the leader stands and yells SMADNESS 5. The team leader shows the rest of the class the proper way to find each number. 6. A second team can challenge the first team s findings. If the first team is wrong, the second team takes the point away from the first team. Ex. The roll consisted of 1, 2, 5, and 5. (2-1)(5/5) = 1 (2-1) + (5/5) = = 3 (5+5)/2-1 = 4 (5+5)/2*1 = 5 (5+5)/2+1 = = *1 = = 9 5*(2+1)-5 = 10 **(from Volume 56, Number 1, 2006 version of Mathematics Teacher Journal) Online version of Smadness Computer Based Learning (great resource if you have computer lab access)

8 Matchmaker Matchmaker Make Me a Match See rules at: Solution Key for Matchmaker Matchmaker Make Me a Match Procedure: Raise your hand if you have a question 1. Cut out all squares 2. Perform the necessary calculations 3. Match the calculations the correct answer 4. Raise your hand when you are finished HANDOUTS HANDOUTS HANDOUTS HANDOUTS HANDOUTS HANDOUTS

9 Bowl A Fact Plastic bowling pins will be set up labeled 1-10 in a triangular shape. Object: Knock as many pins down as possible. Procedure: 1. You are given 3 dice. 2. One student rolls all three dice and uses those three numbers using any operations to reach one of the pin numbers. If a number is reached, the pin is knocked down. Students knock down as many pins as possible with the first three numbers. If you knock down all ten pins, you get a strike. 3. You are allowed a 2 nd roll if all the pins are not knocked down to try and pick up the spare. Scoring ( Here are three examples of scoring for bowling EXAMPLE 1 Frame John Score In Example 1 we omitted strikes and spares for simplicity. Each frame is totaled and added to the cumulative score. EXAMPLE 2 Frame Mary 9-0 3/ 6-1 3/ 8-1 5/ 0/ 8-0 7/ 8/8 Score In Example 2 we learn how to score spares and open frames together. A spare is scored as 10, plus the pinfall of the next ball rolled. This total is added to the cumulative score. Frame 1) Count 9 pins Frame 2) Spare (10), plus next ball (6) added to score = 25 Frame 3) Count 7 pins and add to score = 32 Frame 4) Spare (10), plus next ball (8) added to score = 50 Frame 5) Count 9 pins and add to score = 59 Frame 6) Spare (10), plus next ball (0) added to score = 69 Frame 7) Spare (10), plus next ball (8) added to score = 87 Frame 8) Count 8 pins and add to score = 95 Frame 9) Spare (10), plus next ball (8) added to score = 113 Frame 10) Add (10), plus 8 to score = 131 Example 3 Frame Kim X 3/ 6-1 X X X 2/ 9-0 7/ XXX

10 Score In Example 2 we learn how to score strikes, spares and open frames together. As previously demonstrated, a spare is scored as 10, plus the pinfall of the next ball rolled. A strike is scored as 10, plus the pinfall of the next 2 balls rolled. This total is added to the cumulative score. Frame 1) Strike (10), plus next 2 balls (3)(7) = 20 Frame 2) Spare (10), plus next ball (6) added to score = 36 Frame 3) Count 7 pins and add to score = 43 Frame 4) Strike (10), plus next 2 balls (10)(10) add to score = 73 Frame 5) Strike (10), plus next 2 balls (10)(2) add to score = 95 Frame 6) Strike (10), plus next 2 balls (2)(8) add to score = 115 Frame 7) Spare (10), plus next ball (9) added to score = 134 Frame 8) Count 9 pins and add to score = 143 Frame 9) Spare (10), plus next ball (10) added to score = 163 Frame 10) Strike (10), Strike (10), Strike (10) = 193

11 Object: Reach the Target Number Procedure: Target Number 1. You need 4 dice 2. Roll two of the dice and choose the number you want(ex. If a 3 and 5 come up you can use 35 or 53(target number)). 3. Roll all 4 dice 4. You have to use the 4 numbers that come up and perform math operations to try to get as close as you can to the target number. You are only allowed to use each number once. You can use any operation including squares and square roots. 5. You have one minute to work. When time is up, whoever is closest gets a point. If more than two of you are the closest, you both get a point but the students must have the work written down to get credit. If you should get the target number while working, you must yell out TARGET indicating that you got it. If you did the work correctly, then you get 2 points and you start all over. An example Target number: 45 Numbers Rolled: 1, 3, 5, 6 (6+3) * 5/1 = 45

12 Smadness With your team, create the numbers 1 10 using the four numbers given by the teacher once and only once. You may use any mathematical operation you wish. After your team has all ten numbers, your team leader must stand up and say SMADNESS Round 1 Round 2 Round 3 1= 1= 1= 2= 2= 2= 3= 3= 3= 4= 4= 4= 5= 5= 5= 6= 6= 6= 7= 7= 7= 8= 8= 8= 9= 9= 9= 10= 10= 10=

13 Matchmaker Matchmaker Make Me a Match Procedure: Raise your hand if you have a question 1. Cut out all squares 2. Perform the necessary calculations 3. Match the calculations the correct answer 4. Raise your hand when you are finished